As a second example, we consider RMG with a twin boundary stacking fault, as illustrated in Fig. REF  (right panel) for \(N = 7\)  layers. Specifically, we use integers \((m,n)\)  to denote
a rhombohedral section with \(m\)  layers and sites \(A_1\) , \(B_1\) , ..., \(A_m\) , \(B_m\)  connected by a twin boundary stacking fault to a rhombohedral section with \(n\)  layers and sites \(B_{m}\) , \(A_{m}\) , ...\(B_N\) , \(A_N\)  where \(m \ge 2\) , \(n \ge 2\) . The total layer number is \(N = m+n-1\)  because the two rhombohedral sections `share' the layer with sites \(A_m\) , \(B_m\) .
Thus, the example in Fig. REF  is a \((3,5)\)  twin boundary stacking fault with \(N=7\)  total layers.
This fault contrasts with the Bernal fault. For example, at the stacking fault there are only three vertically connected atomic sites (sites \(B_2\) , \(A_3\) , \(B_4\) , in Fig. REF ) which make up a trimer; this is odd so it contributes two bulk bands and one band near zero energy at \(k=0\)  [1]} in a similar way to trilayer Bernal graphene [2]}. Thus, overall, there are four low energy bands per spin and valley related to three sites not directly connected to a neighbor in an adjacent layer, namely \(A_1\) , \(B_m\) , \(A_{N}\)  (sites \(A_1\) , \(B_3\) , \(A_7\)  in Fig. REF ) plus
an odd combination of trimer sites \((B_{m-1}-B_{m+1})/\sqrt{2}\)  [\((B_{2}-B_{4})/\sqrt{2}\)  in Fig. REF ].
